# Potential energy of a system

1. Feb 8, 2009

### bkl4life

1. The problem statement, all variables and given/known data

The potential energy of a system consisting of two identical charges is 4.5 mJ when their separation is 38 mm.

a) What is the magnitude of each charge?
b) How many individual charges are present in the system? (You can assume the charges are either electrons or protons.)

2. Relevant equations
F=Ke(q1*q2)/r^2

3. The attempt at a solution

I'm not really sure where to start.
Do I need the charge of an electron or proton? Any help would be awesome!

2. Feb 8, 2009

### Hootenanny

Staff Emeritus
The first thing to do is to calculate the potential energy of the system.

What is the definition of [electrical] potential energy?

3. Feb 8, 2009

### bkl4life

I think it's the amount of work needed to separate the charges.

(9 x 10^9)*(1.6*10^-19)*(-1.6*10^-19)/.038
= -6.06 *10^-27

When does the 4.5 mJ come into play

4. Feb 8, 2009

### Hootenanny

Staff Emeritus
Close but not quite. Notice that the question states that the two charges are equal, in which case they would repel and therefore no work would be required to seperate them, they would do so of their own accord.

The potential energy of two charges is the work required to bring the charges from an infinite distance to r = 0.038m.
Are you just pulling numbers out of thin air? Where did you get the values from the charges from?

5. Feb 8, 2009

### bkl4life

I was using the charge of an electron. I was looking at part b when I used those numbers. Should I use the 4.5 mj instead of the charge of electron? The total potential of a system is the sum of all the contributions for each pair of particles. I'm just lost.

6. Feb 8, 2009

### Hootenanny

Staff Emeritus
Why?
I say again. Why? You cannot answer part (b) until you have a solution for part (a).
No, since 4.5 mJ is an energy and not a charge.
Don't worry we can start again. What does your textbook have to say about the potential energy of two point charges?

If your textbook is of no help, try here: http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/elepe.html

I'm going offline now, but I'm sure someone else will be more than happy to jump in and help you. If not, I'll check in later this evening.

7. Feb 8, 2009

### bkl4life

My book says:

U=q'*V
U=electric potential energy
V= electric potential
q'= charge

It also says that:

V=U/q'= K(q/r)

Would I be able to do:

2*(8.99*10^9)(charge)/.038= 4.5 mJ

8. Feb 9, 2009

### Hootenanny

Staff Emeritus
You have the right idea, but here you are calculating the potential of a single charge q', rather than the potential energy of two charges.

Check out the link I gave you above.